Chosen Solution
I replaced the battery in this MBP just over a year ago. It now shuts off immediately when unplugged and Coconut Battery registers no battery at all. Does this indicate a faulty battery or a logic board problem? The latter seems more likely to me, but I’m asking because a battery for another computer of the same model that I ordered from iFixit around the same time last year also recently turned out to be faulty.
Sadly your battery is bad! The micro-controller within it has failed so the communication to your system is not working as well as the charging of the battery. Time to replace it! I would contact the seller to see if they offer a warranty. As an example iFixit offers a year.
Try replacing the battery again. If that doesn’t do the trick, that is when you should either replace the logic board or the whole MacBook altogether.
